Cooking soft-boiled eggs is usually a matter of careful timing and not too much heat. It can be hit-or-miss, so the folks at America's Test Kitchen wanted a more repeatable method that worked every time. The secret? Way less water than you think -- about a centimetre, tops.
The video above is a little long, but it explains the process. Because the beauty of a soft boiled egg is a firm white but a soft yolk, you have to take care with temperature. The whites of an egg set at 82 degrees C while the yolk will cook through if it gets past 70 degrees C. It seems like a catch 22, but the fix is to instead use only a centimetre or so of boiling water (which will re-boil quickly as you add cold eggs to it) in a covered pan, and let most of the egg rest in the steam coming off of that water, which, as steam is, is a regular and constant 100 degrees C. This lets the eggs cook really quickly without giving the yolk time to set.
You'll want to use cold, large eggs -- the recipe will work for however many eggs you want to cook. Six and a half minutes in the water, and that's all there is to it. Watch the video above to see the whole system work, and hear a more scientific description of how the process works.
Perfect Soft Cooked (Soft Boiled) Eggs [America's Test Kitchen (YouTube)]